The optical nonlinear refractive and absorptive parameters of the dye N,N′–Bis(2,5,-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (DBPI) in 96% sulphuric acid have been obtained by a single closed-aperture (CA) Z-scan technique with picosecond pulses at the wavelength of 532 nm. Here a theoretical model was used to deduce both the refractive and absorptive optical nonlinearity present simultaneously in the CA Z-scan profile. Under the range of concentrations and energies studied here, we found that the effect of saturable absorption (SA) is dominating at higher concentrations (i.e. 1.0 × 10−3 M), whereas the reverse saturable absorption (RSA) effect was taken over at dilute concentrations (i.e. 1.0 × 10−4 M and 1.0 × 10−5 M). The dominance of absorptive nonlinearity over the refractive nonlinearity results in a low value of the refractive cross-section (σr). A relative increase in the value of σr is observed with decrease in the dye concentration. Mathematical modeling of CA Z-scan profiles of DBPI shows the existence of peak-valley or valley-peak structure depending upon the contribution of nonlinear absorption. The optical nonlinear parameters have also been estimated by theoretical simulation studies as a function of wavelength and compared with the experimental results. The dye DBPI has been found to be suitable as an important highly photostable molecule for photonic devices in the visible region (400–630 nm). © 2017 Elsevier B.V.